Unlike most other interpretations, I believe being in constant motion means taking up lots of responsibilities. I consider it the difference between Jonathan the Lecturer and Jonathan the President. When our President was a lecturer he had a well defined job role and wasn't rolling about much. But since he became the President he has been doing about a million things, rolling around to fix our national issues. He is now a rolling stone that is not overwhelmed by any one worry because each single day is filled with new worries for him. He can't afford to gather moss or he will be killed by the pressure upon him.
When you have a flexible job or live a not too structure life, you come in touch with lots of ideas and activities. Life becomes fuller and more fun. Nothing can keep you down. You know that no victory is permanent and no failure is final. You have faced so many chilling experiences that you are now immune to a lot of what troubles most people. You are more focused on tomorrow than today. You become an optimist. You even look forward to the future, and not just for what it brings but also what it relieves you of. You don't feel too attached to anything and have a more open mind.
Living a very active life also means you'll get a lot of uncommon opportunities. You'll get to see things from several perspectives and make excellent use of all your skills. You also get to learn a lot of new things and see the strange beauty that lies wherever you go.
A rolling stone gathers no moss. Live a much more active life. Don't forever court the mundane. Roll around, either by physical or mental activities. Don't let you mind be filled with idle thoughts but with creative solutions and thoughts.